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## Comment on

Find the 3-Part Ratio## For the first question - how

a:b:c=2c:3c:6c

*divide both sides by c*

a/c:b/c:c/c=2:3:6

## That isn't how EQUIVALENT

That isn't how EQUIVALENT ratios work.

If we take a ratio (not an equation) and multiply or divide it's PARTS by some non-zero value, we create an EQUIVALENT ratio.

So, for example, we can take the ratio 10 : 35, and divide both parts of the ratio by 5 to get the EQUIVALENT ratio 2 : 7

That is, 10 : 35 = 2 : 7

Likewise, we can take the ratio 2c : 3c : 6c and divide all the parts by c to get 2 : 3 : 6

That is 2c : 3c : 6c = 2 : 3 : 6

So, as the solution tells us...

a : b : c = c/3 : c/2 : c [via substitution]

= 2c + 3c + 6c [we took the previous ratio and multiplied all 3 parts by 6]

= 2 + 3 + 6 [we took the previous ratio and divided all 3 parts by c]

Does that help?

## At 1:41 I'm confused as to

## You're referring to 1:30 in

You're referring to 1:30 in the above video.

Here we must convert c/3 : c/2 : c into an equivalent ratio.

If we multiply each term by 6, we get: 6c/3 : 6c/2 : 6c

When we simplify each term by 6, we get: 2c : 3c : 6c

Now let's see what happens when we DIVIDE each term by 6.

We get: (c/3)/6 : (c/2)/6 : c/6

Rewrite 6 as 6/1 to get: (c/3)/(6/1) : (c/2)/(6/1) : c/(6/1)

Invert and multiply: (c/3)(1/6) : (c/2)(1/6) : c(1/6)

We get: c/18 : c/12 : c/6

While this new ratio is still EQUIVALENT to c/3 : c/2 : c, it doesn't match any of the answer choices.

For more information about eliminating fractional expressions, watch: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Cheers,

Brent

## For this question, does this

Since c / a = 3, then a / c = 1 / 3, meaning, a : c = 1 : 3

Similarly, since c / b = 2, then b / c = 1 / 2, meaning, b : c = 1 : 2

To link a : c to b : c, we will use c. The only way we can link c is to make c in both a multiple of both 3 and 2. Here, we will use 6. In the first ratio, we get a : c = 2 : 6 and in the second ratio, we get b : c = 3 : 6. To put it together, we get a : b : c = 2 : 3 : 6.

Did that approach make sense? Thanks fo your time.

## Hey stomer,

Hey stomer,

That's a completely valid approach. Nice work!

Cheers,

Brent

## Hi, why does the rule 'if a/b

## Everything you stated is

Everything you stated is entirely true (1c = 3a and 1c = 2b), but what steps did you take to conclude that a:b:c = 1:2:3?

Once I see your solution, I'll be able to help more.

Cheers,

Brent

## Sorry, I misspoke above. I

## Be careful. If 1c = 3a, then

Be careful. If 1c = 3a, then a : c = 1 : 3

Here's why.

Take: 1c = 3a

Divide both sides by c to get: 1 = 3a/c

Divide both sides by 3 to get: 1/3 = a/c

In other words, a : c = 1 : 3

Likewise, if 1c = 2b, then b : c = 1 : 2

Cheers,

Brent

## Hi Brent,

This is how I worked this problem.

If c/a=3, then c/a = 3/1 (c=3, a=1 )

If c/b=2 , then c/b = 2/1 (c=2, b=1 )

C is a common term in both ratios, so combine them by creating equivalent ratios.

Multiply first ratio by 2 and second one by 3

c/a = 6/2

c/b = 6/3

From the above, a = 2, c=6 and b = 3

So, a:b:c = 2:3:6.

Please let me know if this works :)

## That approach is perfect.

That approach is perfect. Nice work!

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